CP$^2$: Leveraging Geometry for Conformal Prediction via Canonicalization

TL;DR

This paper introduces CP$^2$, a method that incorporates geometric information like pose canonicalization into conformal prediction to improve uncertainty quantification under geometric data shifts.

Contribution

It proposes a novel approach combining geometric canonicalization with conformal prediction to enhance robustness against geometric shifts in data.

Findings

Improved coverage guarantees under geometric shifts.

Effective across discrete and continuous transformations.

Maintains applicability to black-box models.

Abstract

We study the problem of conformal prediction (CP) under geometric data shifts, where data samples are susceptible to transformations such as rotations or flips. While CP endows prediction models with post-hoc uncertainty quantification and formal coverage guarantees, their practicality breaks under distribution shifts that deteriorate model performance. To address this issue, we propose integrating geometric information--such as geometric pose--into the conformal procedure to reinstate its guarantees and ensure robustness under geometric shifts. In particular, we explore recent advancements on pose canonicalization as a suitable information extractor for this purpose. Evaluating the combined approach across discrete and continuous shifts and against equivariant and augmentation-based baselines, we find that integrating geometric information with CP yields a principled way to address geometric shifts while maintaining broad applicability to black-box predictors.